Question

The perimeter of a triangular field 450 m and its sides are in the ratio 13 12 15 find the area of the triangle

Answer 1

Answer:

⇒ Area = 6750 m²

Step-by-step explanation:

It is given that two sides a, b, c of the triangle are in the ratio 13 : 12 : 5. i.e.,

a : b : c = 13 : 12 : 5

⇒a = 13x , b = 12x, c = 5x

Therefore,

⇒ 2s = 450 = 13x + 12x + 5x

⇒ 450 = 30x

⇒ x = 450/30 = 15

So, the sides of the triangle are:

a = 13 × 15 = 195 m

b = 12 × 15 = 180 m

c = 5 × 15 = 75 m

It is given that perimeter = 450

⇒ 2s = 450

⇒ s = 450/2 = 225

Hence,

⇒ Area = √s ( s - a ) ( s - b ) ( s - c )

⇒ Area = √225 ( 225 - 195 ) ( 225 - 180 ) ( 225 - 75 )

⇒ Area = √ 225 × 30 × 45 × 150

⇒ Area = √5² × 3² × 3 × 5 × 2 × 3² × 5 × 5² × 2 × 3

⇒ Area = 5 × 5² × 3² × 3 × 2

⇒ Area = 6750 m²